Mathematics · 2023
JEE Main · 1 February 2023, Shift 2 · Q61
Let P(S) denote the power set of S={1,2,3, ….., 10}. Define the relations R_1 and R_2 on P(S) as AR_1 B if ( A ∩ B^c ) ∪( B ∩ A^c )=∅ and AR_2 B if A…
Let $\displaystyle P(S)$ denote the power set of $\displaystyle S=\{1,2,3, \ldots . ., 10\}$. Define the relations $\displaystyle R_1$ and $\displaystyle R_2$ on $\displaystyle P(S)$ as $\displaystyle \mathrm{AR}_1 \mathrm{~B}$ if $\displaystyle \left(\mathrm{A} \cap \mathrm{B}^{\mathrm{c}}\right) \cup\left(\mathrm{B} \cap \mathrm{A}^{\mathrm{c}}\right)=\emptyset$ and $\displaystyle \mathrm{AR}_2 \mathrm{~B}$ if $\displaystyle \mathrm{A} \cup \mathrm{B}^{\mathrm{c}}=\mathrm{B} \cup \mathrm{A}^{\mathrm{c}}, \forall \mathrm{A}, \mathrm{B} \in \mathrm{P}(\mathrm{S})$. Then :
Official answer
From NTA’s final answer key for this paper.
(2)
both $\displaystyle \mathrm{R}_1$ and $\displaystyle \mathrm{R}_2$ are equivalence relations
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JEE Main 2023 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.